WASHINGTON (CNN) --Under fire for saying that the United States should be even-handed in the Israeli-Palestinian dispute, 2004 Democratic presidential front-runner Howard Dean Wednesday said he would not abandon the long-standing policy of strong U.S. support for Israel.

The former Vermont governor said criticism of his remarks by presidential rival Sen. Joseph Lieberman was a "despicable" attempt to divide the Democratic Party, which has long enjoyed the support of many Jewish voters.

"We do have a special relationship with Israel. We would defend Israel if necessary. I think that is well-known," he told CNN. "However, we are also the only country capable of bringing peace to the Middle East, and when we sit at the negotiating table, we do have to have the trust of both sides or we will never succeed."

Dean also called on President Bush to "swallow his pride" and send former President Bill Clinton to the Middle East to salvage the peace process.

"I think Bill Clinton is the president who has come the closest to bringing Israelis and Palestinians together," he said. "Bill Clinton may just be the person we need to put those negotiations back on track."

The controversy began last week when Dean, speaking about the Middle East, said he didn't "believe stopping the terror has to be a prerequisite for talking. You always talk."

He went on to say that "it's not our place to take sides" and said "enormous" numbers of Israeli settlements in Palestinian territories would have to be dismantled.

Tuesday night during a debate in Baltimore, Lieberman pounced on Dean, saying he was abandoning more than 50 years of bipartisan U.S. policy offering unconditional support to Israel. (More on debate)

'Palestinians are more surprised than anyone'

Lieberman kept up the pressure Wednesday in a speech to the Council on Foreign Relations in New York.

"When you start to say, in very loaded terms -- particularly when Israelis are under assault by terrorists, not unlike the situation we find ourselves in -- that America shouldn't take sides in the Israeli-Palestinian dispute, that's a break in more than half a century of the American foreign policies carried out by presidents of both parties, and it's very harmful," he said.

"I bet the Palestinians are more surprised than anyone else when they heard Howard Dean say this."

Several Democratic leaders of Congress, including House Minority Leader Nancy Pelosi, also circulated a letter Wednesday taking issue with Dean's comments.

But Dean insists that what he was saying was that the United States should serve as a impartial broker between the two sides in order to reach a peace deal -- the same policy pursued by Clinton.

"When you're at the negotiating table, you don't sit down and blame people when you're negotiating," he said. "There's a difference between our policy in Israel -- which has always been supportive, including the willingness to defend Israel -- and what you do at the negotiating table, which clearly has to have the trust of both sides."

'Perhaps I could have used a different euphemism'

Dean also said he would "strongly speak out against violence of any kind in the Middle East. That's what I mean by being even-handed." (More on violence)

"You must condemn all civilian killings, including any terrorist attacks," he said.

However, in retrospect, Dean said he should not have used the term "even-handed."

"I've since learned that that is a very sensitive word to use in certain communities, so perhaps I could have used a different euphemism," he said. "But the fact of the matter is, at the negotiating table, we have to have the trust of both sides."

Asked about the dismantling of Jewish settlements, Dean said that was an issue to be decided during negotiations between the two sides, although he said even the Israelis have conceded that some settlements will have to go.

Asked if he would oppose the Israeli policy of selectively killing leaders of Hamas and other Palestinian militant groups, Dean said, "I think no one likes to see violence of any kind."

But he also said that "there is a war going on in the Middle East, and members of Hamas are soldiers in that war, and, therefore, it seems to me that they are going to be casualties if they are going to make war."

Another comment by Dean has ignited controversy.

In Wednesday's debate, sponsored by the Congressional Black Caucus and the Fox News Channel, Dean said, "I'm the only white politician that ever talks about race in front of white audiences."

Another of his presidential rivals, Sen. John Edwards of North Carolina, took issue with those remarks, saying he frequently talks about race in front of white audiences. CNN has verified that Edwards, indeed, has made such comments.

Asked about Edwards' criticism, Dean said, "I don't know what his context is, but I said exactly what I said last night at Jesse Jackson's PUSH forum out in Chicago about two months ago, and I never heard a peep from any of these candidates about that."

"I think a lot of this stuff is motivated by my position in the polls right now, and that's part of politics. I don't think it's a good part of politics, though."